Consider the two relative frequency histograms.

Consider the two relative frequency histograms. Grae A Gauri 8 Histogram A Histogram 8 Relative frequency Relative frequency 0.20 0.20 Os 0.15 0.10 0.10 0.05 00s 0.0 0.0 0.10 T T T T 0.35 5 0.20 0.25 0.30 0.35 proportion for samples of size 70 T T T T ols 020 025 030 Sample proportion for samples of size 40 @ @ Histogram A was constructed by selecting 100 different random samples of size 40 from a population consisting of 20% part-time students and 80% full-time students. For each sample, the sample proportion of part-time students, p , was calculated. The 100 p values were used to construct the histogram. Histogram B was constructed in a similar way, but using samples of size 70. (a) Which of the two histograms indicates that the value of p has smaller sample-to-sample variability? How can you tell? Histogram B indicates that the value of p has smaller sample-to-sample variability than Histogram A because Histogram B has values that tend to deviate less from the center than Histogram A, indicating a smaller standard deviation of the values of p. Histogram A indicates that the value of p has smaller sample-to-sample variability than Histogram 8 because Histogram A has values that tend to deviate less from the center than Histogram B, indicating a larger standard deviation of the values of p. Histogram B indicates that the value of p has smaller sample-to-samople variability than Histogram A because Histogram B has values that tend to deviate more from the center than Histogram A, indicating a larger standard deviation of the values of p. Histogram A indicates that the value of p has smaller sample-to-sample variability than Histogram B because Histogram A has values that tend to deviate more from the center than Histogram 8, indicating a larger standard deviation of the values of p. OHistogram A indicates that the value of p has smaller sample-to-sample variability than Histogram 8 because Histogram A has values that tend to deviate less from the center than Histogram B, indicating a smaller standard deviation of the values of p. (b) For which of the two sample sizes, n = 40 or m = 70, do you think the value of p would be less likely to be close to 0.20? What about the given histograms supports your choice? Osamples of size n = 70 would yield a value of # that is less likely to be close to 0.20 because the histogram for n = 70 seems to have less sample-to-sample variability. Samples of size n = 70 would yield a value of p that is less likely to be close to 0.20 because the histogram for n = 70 seems to have more sample-to-sample variability. Samples of size n = 40 would yield a value of p that is less likely to be close to 0.20 because the histogram for n = 40 seems to have more sample-to-sample variability. Osamples of size mn = 40 would yield a value of p that is less likely to be close to 0.20 because the histogram for n = 40 seems to have less sample-to-sample variability. Samples of size n = 40 would yield a value of p that is less likely to be close to 0.20 because the histogram for n = 40 is not centered at 0.20